Singlet fission dynamics modulated by molecular configuration in covalently linked pyrene dimers, Anti- and Syn-1,2-di(pyrenyl)benzene

Covalently linked dimers (CLDs) and their structural isomers have attracted much attention as potential materials for improving power conversion efficiencies through singlet fission (SF). Here, we designed and synthesized two covalently ortho-linked pyrene (Py) dimers, anti- and syn-1,2-di(pyrenyl)benzene (Anti-DPyB and Syn-DPyB, respectively), and investigated the effect of molecular configuration on SF dynamics using steady-state and time-resolved spectroscopies. Both Anti-DPyB and Syn-DPyB, which have different Py-stacking configurations, form excimers, which then relax to the correlated triplet pair ((T1T1)) state, indicating the occurrence of SF. Unlike previous studies where the excimer formation inhibited an SF process, the (T1T1)’s of Anti-DPyB and Syn-DPyB are formed through the excimer state. The dissociation of (T1T1)’s to 2T1 in Anti-DPyB is more favorable than in Syn-DPyB. Our results showcase that the molecular configuration of a CLD plays an important role in SF dynamics.

4 fundamental light onto a 1 mm path length quartz cell containing water, was used as a probe beam. The white light was directed to the sample cell with an optical path of 2.0 mm and detected with a CCD detector installed in the absorption spectroscopy system after the controlled optical delay. The pump pulse was chopped by a mechanical chopper synchronized to one-half of the laser repetition rate, resulting in a pair of spectra with and without the pump, from which the absorption change induced by the pump pulse was estimated.
Fluorescence excitation spectra: We also checked the possibility that Py molecules are present as impurities in Anti-DPyB and Syn-DPyB solutions. Py molecule shows a strong fluorescence in solutions. Therefore, if Py molecules are present as impurities in Anti-DPyB and Syn-DPyB solutions, they may contaminate the fluorescence spectra from the Anti-DPyB and Syn-DPyB samples. To check this possibility, we measured the fluorescence excitation spectra of Anti-DPyB and Syn-DPyB in acetonitrile at two emission peak positions (380 and 480 nm). As can be seen in Supplementary Figure S8, the fluorescence excitation spectra from Anti-DPyB and Syn-DPyB are significantly different from the absorption spectrum of Py molecule. This result indicates that Py molecules do not exist as impurities in Anti-DPyB and Syn-DPyB solutions. Although the fluorescence excitation spectra at the two peak emission positions for Anti-DPyB are similar (Supplementary Figure S8A), their maximum peak positions are different; 329 nm for the 380-nm fluorescence excitation spectra and 344 nm for the 480-nm one. Accordingly, the two fluorescence excitation spectra have different ratios of the intensity at 329 nm to that at 344 nm, which suggests that two emission bands of 380 and 480 nm originate from two different emissive states. In addition, the two fluorescence excitation spectra are similar to the absorption spectrum of Anti-DPyB. In contrast to Anti-DPyB, the fluorescence excitation spectra measured at the two emission wavelengths (380 and 480 nm) of Syn-DPyB originating from the two emissive states (monomeric S1 and excimer states) are significantly different from each other (Supplementary Figure S8B). The fluorescence excitation spectrum for the 380 nm emission is similar to the absorption spectrum of Anti-DPyB, which has a monomeric character, whereas the fluorescence excitation spectrum for the 480 nm emission is similar to the absorption spectrum of Syn-DPyB, respectively, indicating that two emission bands of 380 and 480 nm originate from two different emissive states. This result further supports our conclusion based on the emission spectra that the dual emissions (~380 and 480 nm) from Anti-DPyB and Syn-DPyB come from two emissive states, Py monomer moieties and the excimer.

Triplet quantum yield (ΦT) of Anti-DPyB:
We estimated the triplet quantum yield (ΦT) of Anti-DPyB in n-hexane and acetonitrile using nanosecond TA spectroscopy. ΦT was calculated using the following supplementary equation (S1), (S1) 5 where ΔASample and ΔARef are the delta absorbances of the sample and the reference measured by nanosecond TA experiment, respectively. ΦT and ΦT_Ref represent the triplet quantum yields of the sample and the reference sample, respectively. εT_Sample (Py) and εT_Ref are the triplet extinction coefficients of pyrene (Py) and the reference sample, respectively. AbsSample and AbsRef are the absorbances of the sample and the reference sample at 355 nm, respectively. The triplet quantum yield (ΦT_Ref = 1) of benzophenone was used for ΦT_Ref. It is known that the εT value of Py in benzene is 20900 M -1 cm -1 at 420 nm and the εT value of benzophenone in benzene is 7630 at 532.5 nm. 3 Since it is generally known that the effect of solvents on the triple extinction coefficient of a solute molecule is small, we used the εT values of Py and benzophenone measured in benzene to determine the ΦT values of Anti-DPyB in n-hexane and acetonitrile. From the nanosecond TA experiment, the ΦT values of Anti-DPyB in n-hexane and acetonitrile are determined to be 44.1 and 17.5%, respectively.

Time-resolved EPR spectroscopy:
The TR-EPR measurements were carried out at Korea Basic Science Institute (KBSI) in Seoul, Korea. Anti-DPyB and Syn-DPyB were dissolved in toluene, and the sample concentrations were adjusted to 2 mM. The sample solutions were degassed by purging with N2 gas for 1.5 h and transferred to EPR tubes via cannula using Schlenk techniques under an N2 atmosphere. The transferred solutions were immediately frozen in liquid N2. The photoexcitations were performed by the third harmonics (355 nm) of a nanosecond Q-switched Nd:YAG laser (Continuum, Surelite-I). The laser power used in this work was 6 mJ at the 10 Hz repetition rate. Time-resolved EPR data were obtained on a Bruker Elexsys E580 spectrometer, and the cryogenic temperature was achieved with an Oxford CF-935 cryostat and Oxford ITC temperature controller. X-band (9.728 GHz) transient EPR data were acquired using a Bruker 4118X-MD5 dielectric ring resonator and Q-band (34 GHz) time-resolved pulsed EPR were collected using an EN5107D2 resonator.
X-band CW (continuous wave) transient EPR experiments were performed by direct detection at a temperature of 80 K with a microwave power of 15 mW. The laser was triggered by an external digital pulse delay generator, and the delay times were adjusted to 160-200 ns. The background signal from the laser was removed by 2D baseline correction determined based on the off-resonance transients. 34 GHz time-resolved ESE (electron spin echo) detected spectra were carried out using the pulse sequence, laser-Tdelay-π/2-τ-π-τ-echo, with microwave pulse lengths of 16-32 ns and an inter-pulse time of τ = 200 ns. The pulsed EPR measurements were conducted at 80 K. All experimental spectra were simulated using EasySpin. 4 Supplementary Figure S20 shows EPR spectra of Anti-DPyB and Syn-DPyB at 128 and 200 ns after photoirradiation. The EPR signals for Anti-DPyB and Syn-DpyB show the narrow peak splitting of 34 and 19 mT around 340 mT (g = 2.002), respectively. In addition to the narrow peak splitting, Anti-DPyB and Syn-DPyB exhibit a large peak splitting of 150 and 115 mT, respectively. The EPR signal for Anti-DPyB is well reproduced by the simulated curve for its triplet using EasySpin with zero-field splitting (ZFS) parameters of D = -2399 MHz and E = 480 MHz. Similarly, the EPR signal for Syn-DPyB is well reproduced by the simulated curve for its triplet using EasySpin with ZFS parameters of D 6 = -1890 MHz and E = 450 MHz. These consistencies suggest that the EPR signals measured from Anti-DPyB and Syn-DPyB arise from triplet (S = 1) species. To further confirm the origins of TR-EPR signals, the nutation experiment for Q-band (34 GHz) TR-EPR signal of Anti-DPyB was measured using the pulse sequence, laser-Tdelay-π/2-τ-π-τ-echo, with microwave pulse lengths of 16 -32 ns and an inter-pulse time of τ = 200 ns. As shown in Supplementary Figure S21A, Q-band (34 GHz) TR-EPR spectrum of Anti-DPyB shows a microwave emission (E)/absorption (A) polarized pattern similar to X-band EPR spectrum. It is known that in the extremely weak limit of the microwave irradiation field (B1 = w1/g), the nutation frequency wn of spin magnetization is simply given by wn = w1[S(S + 1) -ms(ms -1)] 1/2 for a transition |S, ms〉 ↔ |S, ms -1〉. In this experiment, w1 is 8.5 MHz. The wns for EPR peaks of 1131. 5, 1195.3,1229.7, and 1293.0 mT are determined to be all 11.74 MHz. The observed nutation frequency ratios wn/w1 are ~1.4, consistent with the theoretical value corresponding to the T0 → T±1 transition. This result supports that the EPR signal measured from Anti-DPyB is attributed to triplet species. Although the nutation measurement on the EPR signal of Syn-DPyB was not performed, we speculate that the X-band EPR signal measured from Syn-DPyB arises from triplet species as well. The EPR signals at a few hundred nanoseconds do not show evidence for (T1T1). The absence of EPR signals of (T1T1) for Anti-DPyB and Syn-DPyB at a few hundred nanoseconds is probably due to the shorter lifetimes of (T1T1)s than the temporal resolution (~120 ns) of our TR-EPR system. The femtosecond TA measurements show that the time profile for transient absorption bands of Anti-DPyB around 440 nm, which well reflects the relaxation kinetics of (T1T1), shows slow but distinct rising features (Supplementary Figure S19A), suggesting that the lifetime of (T1T1) for Anti-DPyB is longer than 10 ns. Compared with Anti-DPyB, Syn-DPyB shows a relatively fast decay feature in the time profile for transient absorption bands of 450 nm (Supplementary Figure S19B). As shown in Table 2, the (T1T1)s of Syn-DPyB in n-hexane and acetonitrile relax to 2T1 and S0 in parallel with time constants of 6.4 and 4.8 ns, respectively, indicating that the lifetime of (T1T1) for Syn-DPyB should be significantly shorter than the temporal resolution (~120 ns) of our TR-EPR system. Meanwhile, we could not precisely determine the lifetime of (T1T1) for Anti-DPyB because of the limited range of investigated delay times in the femtosecond TA measurement. Overall, the EPR data lead us to conclude that the lifetime of (T1T1) for Anti-DPyB should be shorter than the temporal resolution (~120 ns) of our TR-EPR system.

Singular value decomposition (SVD) analysis:
We applied the SVD analysis to our experimental data in the λ range of 400-700 nm. From the experimental TA spectra measured at various time delays, we can build an nλ × nt matrix A, where nλ is the number of λ points in the TA spectrum at a given time-delay point (253 wavelength points for Anti-DPyB and Syn-DPyB) and nt is the number of time-delay points (662 time delay points in the wavelength range from 400 nm to 700 nm for Anti-DPyB and Syn-DPyB). Then, the matrix A can be decomposed while satisfying the relationship of A = USV T , where U is an nλ × nt matrix whose columns are called left singular vectors (lSVs) (i.e. time-independent λ spectra) of A, V is an nt × nt matrix whose columns are called right singular vectors (rSVs) (i.e. amplitude changes of U as time evolves) of A, and S is an nt × nt diagonal matrix whose diagonal elements are called singular values of A and can possess only non-negative values. The matrices U and V have the properties of U T U = Int and V T V = Int, respectively, where Int is the identity matrix. Since the diagonal elements (i.e. singular values) of S, which represent the weight of left singular vectors in U, are ordered so that s1 ≥ s2 ≥ ····· ≥ sn ≥ 0, (both left and right) singular vectors on more left are supposed to have larger contributions to the constructed experimental data. In this manner, we can extract the time-independent transient absorption components from the lSVs and the time evolution of their amplitudes from the rSVs. The former, when combined together, can give information on the TA spectra of distinct transient species, while the latter contains information on the population dynamics of the transient species.
The singular values and autocorrelations of the corresponding singular vectors suggest that the first np singular vectors are enough to represent our experimental data because the contribution of each singular vector (lSV or rSV) to the data is proportional to its corresponding singular value and the autocorrelation of U or V matrix can serve as a good measure of the signal-to-noise ratio of the singular vectors (in this study, four and three significant singular components for the data of Anti-DPyB and Syn-DPyB, respectively). In other words, the contribution from the (np + 1)th singular vectors and beyond becomes negligible. The SVD analysis results are shown in Figure  S11 (Anti-DPyB in n-hexane and acetonitrile), Supplementary Figure S12 (Syn-DPyB in n-hexane and acetonitrile).
To extract kinetic information, as many rSVs as np multiplied by singular values were fit by a sum of multiple exponentials sharing common relaxation times as follows: where so is oth singular value,Vo,fit(t) are oth rSVs try to fit, t are time delays, cn is constant for Vo,fit(t) offset, m is the number of exponential functions, Ai,o is amplitude for ith exponential of Vo,fit(t), ti is ith sharing relaxation times. The Vo,fit(t) are optimized by minimizing discrepancy (quantified by the test function, TF), which is the sum of the every residual between Vo,fit(t) and oth rSVs, Vo(t), as following: To find an appropriate number of exponentials, we performed the fitting by changing the number of exponentials. In the case of Anti-DPyB, the slowest exponential relaxation time did not converge during fitting due to the limited range of time delays, so the slowest relaxation time was fixed to 10 ns. The first four rSVs were simultaneously fitted with a sum of exponential functions with shared relaxation times. A tetra-exponential functions with the shared time constants of 3.6 ± 0.3 ps, 231 ± 19 ps, 1.75 ± 0.12 ns, and >10 ns in n-hexane and 2.8 ± 0.1 ps, 24.3 ± 0.5 ps, 495.7 ± 6.5 ps, and >10 ns in acetonitrile gave satisfactory fits as shown in Supplementary Figures S13A and S131B, respectively. Vo,fit(t) with less than four exponential functions could not provide a satisfactory fit to Vo for Anti-DPyB. Vo,fit(t) with more than four exponential functions could fit Vo, but some exponential time constants show no meaningful difference, indicating that they were overfitted. The obtained relaxation time are 3.6 ± 0.3 ps, 231 ± 19 ps, 1.75 ± 0.12 ns, and > 10 ns in n-hexane and 2.8 ± 0.1 ps, 24.3 ± 0.5 ps, 495.7 ± 6.5 ps, and > 10 ns in acetonitrile. In the case of Syn-DPyB, the first three rSVs were simultaneously fitted with a sum of exponential functions with shared relaxation times. A tri-exponential functions with the shared time constants of 2.3 ± 0.8 ps, 9.7 ± 0.5 ps, and 6.4 ± 0.2 ns in n-hexane; 2.8 ps, 8.0 ± 0.6 ps, and 4.8 ± 0.2 ns in acetonitrile gave satisfactory fits as shown in Supplementary Figures S13C and S13D, respectively. Vo,fit(t) with less than three exponential functions could not provide a satisfactory fit to Vo for Anti-DPyB. Vo,fit(t) with more than four exponential functions could fit Vo, but some exponential time constants show no meaningful difference, indicating that they were overfitted. As mentioned in the main text, the obtained relaxation time are 2.3 ± 0.8 ps, 9.7 ± 0.5 ps, and 6.4 ± 0.2 ns in n-hexane; 2.8 ps, 8.0 ± 0.6 ps, and 4.8 ± 0.2 ns in acetonitrile.

Kinetic analysis:
Using the first a few singular vectors of significant singular values (that is, np principal singular vectors) obtained from the SVD analysis of the experimental data, we performed kinetic analysis. New matrices, U', V', and S', can be defined by removing non-significant components from U, V, and S, respectively. In other words, U' is an nλ × np matrix containing the first np left singular vectors of U, V' is an nt × np matrix containing the first np right singular vectors of V, and S' is an np × np diagonal matrix containing the first np singular values of S. Here we represent the time-dependent concentrations of transiently formed intermediate species, which can be calculated from a kinetic model, by a matrix C. Then, the matrix C can be related to V' by using a parameter matrix P that satisfies V' = CP, where C is an nt × np matrix whose columns represent time-dependent concentrations of transiently formed intermediate species and P is an np × np matrix whose columns contain coefficients for the time-dependent concentrations so that the linear combination of concentrations of the np intermediates can form the np right singular vectors in V', respectively. Once C is specified by a kinetic model with a certain set of variable kinetic parameters such as rate coefficients, P and C can be optimized by minimizing the discrepancy between V' (from the experiment) and CP (from the kinetic theory).
Since V' = CP, the following relationships hold: where A' is an nλ × nt matrix that contains the theoretical TA spectrum ΔA(λi,tj) at given λ and t values. Theoretical TA spectra calculated by using Supplementary Equation (S4) were compared with the experimental TA spectra, and the matrix P and C were optimized by minimizing the discrepancy (quantified by least-square, LS) between the theoretical and experimental TA spectra using the Minuit 1 package: ΔAexp(λi,tj) and ΔAthe(λi,tj) are the experimental and theoretical TA spectrum at a given point of (λi,tj), respectively. From Supplementary Equation (S4), we can define a matrix B as B = U'S'P T , that is, a linear combination of the np left singular vectors in U' weighted by their singular values in S' with their ratios determined by P. Then, the matrix E, an nt × np matrix, contains the np timeindependent TA spectra directly associated with the np intermediate species. Therefore, by optimizing the matrices P and C, we obtain both the time-dependent concentrations (see the optimized C for the kinetic model in Figures 4C, 4D, 5C and 5D) and the time-independent TA spectra of the intermediate species (see the optimized P for the kinetic model in Figures 5A, 5B, 6A and 6B).
For the kinetics analysis of the TA spectra for Anti-DPyB and Syn-DPyB, we considered various plausible kinetic models. For Anti-DPyB, considering five principal components from SVD analysis (Supplementary Figure S11) and four time constants obtained from the fitting of rSVs ( Figure S13), we can set up the simplest kinetic model with five intermediates assigned to FC, S1, excimer, (T1T1), and 2T1 and four time constants connecting them. In this kinetic model, the molecules in the (T1T1) state decay only to 2T1. In fact, they can also decay to S0 as well, and such a case is also compatible with the SVD results. Therefore, one more time constant for the transition from (T1T1) to S0 should be added. The resulting kinetic model is Kinetic Model (1) in Figure 4 of the main text. As the SVD results showed that the lifetime of (T1T1) is longer than 10 ns, we fixed two time constants for the process from (T1T1) to the ground state (4) and the dissociation process of (T1T1) to free triplets (5) as a sufficiently large number, 10 ns. Five SADS curves, population changes for five intermediates (FC, S1, excimer, (T1T1), and 2T1), the experimental TA spectra, the best-fit spectra, and the residuals between them for Anti-DPyB in nhexane and acetonitrile are shown in Supplementary Figures S22 and S23, respectively. The residuals are small, suggesting that the measured TA spectra for Anti-DPyB are well constructed as a linear combination of the five SADS curves.
While Kinetic Model (1) can explain the TA data well, it cannot explain the emission behavior, three time constants and emission quantum yields from emission experiments ( Table 1). The fluorescence decay profiles showed two time constants assigned to the fluorescence lifetimes of the Py monomeric unit and excimer. By adding these two fluorescence decay times to Kinetic Model (1), we set up a new kinetic model (Kinetic Model (2) in Figure 4 of the main text). In this kinetic model, we also included the backreaction from the (T1T1) to the excimer for the following reason. As shown in the inset of Figure 2A, the rising time of 1.24 ns in the fluorescence decay profile for Anti-DPyB in n-hexane is approximately five times larger than the time constant (0.23 ns) corresponding to the S1  excimer transition determined from femtosecond TA experiments. This difference indicates that the observed excimer fluorescence is not the prompt emission but the delayed emission, suggesting the equilibrium between the excimer state and the (T1T1) state. In summary, Kinetic Model (2) has seven time constants and five intermediates. For the backreaction from (T1T1) to the excimer in n-hexane, the time constant of 1.24 ns was used. Unlike in n-hexane, no rising feature was observed in acetonitrile, implying that the process from (T1T1) state to excimer state is faster than the temporal resolution (50 ps) of our time-resolved fluorescence measurement system. Thus, we assumed that the backreaction process from (T1T1) to the excimer in acetonitrile occurs with a time constant of 50 ps. Figure 4 shows the five SADS curves and population changes for five intermediates (FC, S1, excimer, (T1T1), and 2T1), and Supplementary Figure S24 shows the experimental TA spectra, the best-fit spectra, and the residuals between them for Anti-DPyB in n-hexane and acetonitrile obtained from the kinetic analysis using Kinetic Model (2). The residuals between the experimental and the best-fit spectra are small, suggesting that the measured TA spectra for Anti-DPyB are well constructed as a linear combination of the five SADS curves according to the employed kinetic model (Kinetic Model (2)). As the fit qualities of both Kinetic Model (1) and Kinetic Model (2) are comparable, fit qualities alone cannot tell which kinetic model is better. As discussed above and in the main text, however, Kinetic Model (2) is preferred because it is more consistent with the emission data.
For Syn-DPyB, considering the three exponential time constants obtained from the exponentials fitting of rSVs (Supplementary Figure S13), the two time constants and emission quantum yields from emission experiments (Table 1), and four principal components from SVD analysis results (Supplementary Figure S12), we can preferentially set up a kinetic model with five time constants and four intermediates. In addition, the TR-EPR signal for Syn-DPyB indicates that the (T1T1) of Syn-DPyB also dissociates to free triplets. Based on this result, the (T1T1)  2T1 transition was included to the kinetic model. We also included the backreaction from (T1T1) to the excimer as in Anti-DPyB. Consequently, like Anti-DPyB, we used the kinetic model with five intermediates assigned to FC, S1, excimer, (T1T1), and 2T1 (see Figure 4). In the case of Syn-DPyB, it is noteworthy that the τ2 time constant corresponding to the S1 → excimer transition was not resolved in Syn-DpyB ( Table 2). As discussed in the main text, the excimer of Syn-DPyB with a pre-stacked structure is likely to form fast within a subpicosecond (≤ 200 fs) or with a time constant comparable to IVR (3 ps). In this regard, we considered two kinetic models (Kinetic Models (3) and (4) in Figure 4 of the main text). In the former kinetic model, the S1  excimer transition occurs in subpicosecond (≤ 200 fs), and in the other kinetic model, the S1  excimer transition occurs with a time constant comparable to IVR (3 ps). Five SADS curves, population changes for five intermediates (FC, S1, excimer, (T1T1), 2T1), and residuals from the kinetic analysis using Kinetic Model (3) are shown in Supplementary Figure S25. Figure 6 shows the five SADS curves and population changes for five intermediates (FC, S1, excimer, (T1T1), and 2T1) for Syn-DPyB obtained from the kinetic analysis for Kinetic Model (4) in n-hexane and acetonitrile. Supplementary Figure S26 shows the experimental TA spectra, the simulated spectra by a linear combination of the four SADS curves according to Kinetic Model (4), and residuals for Syn-DPyB in n-hexane and acetonitrile. As shown in Supplementary Figures S25 and S26, both Kinetic Models (3) and (4) show small residuals, suggesting that the measured TA spectra for Syn-DPyB are well constructed as linear combinations of the four SADS curves according to both kinetic models. Since the fit qualities of both kinetic models are comparable, fit qualities alone cannot tell which kinetic model is better. Nevertheless, the SADS curves from the two kinetic models are different and provide clues on which kinetic model is better. Whereas the SADS for the S1 state from Kinetic Model (4) is positive (Figure 6), that from Kinetic Model (3) is strongly negative (Supplementary Figure S21). Since a negative SADS is not possible for ESA (excited state absorption) from the S1 state, Kinetic Model (3) can be ruled out. In other words, the kinetic analysis suggests that the S1  excimer transition in Syn-DPyB occurs with a time constant comparable to IVR (3 ps).
Consideration for direct SF mechanisms from the S1 state: It was also reported that the intermolecular and intramolecular SF dynamics could rapidly occur with a direct process from S1 state to the free state due to strong coupling between the S1 state and the free triplet state. 5,6,7 For example, Dover et al. suggested that the SF channel is dominated by a direct mechanism from the S1 state and the formation of the excimer state inhibits the efficient SF dynamics. 7 Thus, we also checked the possibility that our data from Anti-DPyB can be explained with the same direct mechanism. Assuming that the assignment of the five intermediates to FC, S1, excimer, (T1T1), and 2T1 is valid, we can consider a kinetic model that the direct SF process from the S1 state to the free triplet state occurs with a time constant of τ2. In this kinetic model (Kinetic Model depicted in Supplementary Figure S27), the second time constant (τ2) observed from Anti-DPyB can be assigned to the SF dynamics from the S1 state to free triplet state while other time constants of τ1, τ3, and τ4 are assigned to the IVR, the S1 → excimer transition, and the excimer → (T1T1) transition, respectively. The (T1T1) → 2T1 transition (τ5) is excluded to fully reflect the nature of the direct SF process to form the free triplets directly from the S1 state. We analyzed the TA spectra of Anti-DPyB in acetonitrile with this kinetic model (Kinetic Model depicted in Supplementary Figure  S27). Supplementary Figure S28 shows the SADS curves, population changes for five intermediates (FC, S1, excimer, (T1T1), and 2T1), and residuals for Anti-DPyB in acetonitrile according to Kinetic Model depicted in Supplementary Figure S27. The residuals between the experimental TA spectra and the best-fit spectra are not negligible (Supplementary Figure S28), meaning that unlike Kinetic Model (2), Kinetic Model (S1) involving a direct SF process does not reproduce well the measured TA spectra for Anti-DPyB in acetonitrile. This result indicates that the direct SF mechanism occurring with the τ2 time constant does not reproduce well the measured TA spectra for Anti-DPyB in acetonitrile. The fit quality could be improved when in this kinetic model (Kinetic Model (S1)), the direct SF process from the S1 state to the free triplet state is forced to occur with a low reaction yield (50%). But, the SADS for (T1T1) is strongly negative, which is not possible for ESA from (T1T1) (data not shown). Thus, this kinetic model can be ruled out. As another possibility, we also considered a kinetic model that the direct SF process and IVR in FC state simultaneously occur with a time constant of τ1. In this kinetic model, the first time constant (τ1) observed from Anti-DPyB can be assigned to the direct SF dynamics from the FC state to the free triplet state and IVR while other time constants (τ2 -τ4) are assigned as in the reaction mechanism we propose (Kinetic Model (2)). This direct SF mechanism from the FC state to the free triplet state occurring with the τ1 time constant does not reproduce well the measured TA spectra for Anti-DPyB in acetonitrile (data not shown). These results indicate that the τ1 and τ2 time constants observed from Anti-DPyB cannot be attributed to the time constant for the direct SF process. If the SF dynamics in Anti-DPyB occurred with a direct mechanism, those CLDs would be likely to show efficient SF dynamics due to the fast SF process from the S1 state to the free triplet state. However, as explained in the main text, the SF dynamics of anti-DPyB shows the low triplet quantum yield in n-hexane and acetonitrile (44.1 in n-hexane and 17.5% in acetonitrile) and Syn-DPyB does not exhibit any absorption band in both n-hexane and acetonitrile, suggesting that the SF dynamics in Anti-DPyB and Syn-DPyB are not efficient. These results suggest that the SF dynamics of Anti-DPyB and Syn-DPyB cannot be explained by a direct SF mechanism.
The lack of the direct SF process in our data is also evident in the time profiles for transient absorption bands of Anti-DPyB around 440 nm, which corresponds to the T-T absorption band showing slow rising features ( Figure S19A). Fitting the time profiles to an exponential function yields the rising times of > 10 ns and 461 ps in n-hexane and acetonitrile, respectively. These rising times indicate that in Anti-DPyB, the SF process to form free triplets occurs too slowly to be assigned to the direct SF process. The rising times (> 1 ns) are significantly slower than two time constants (τ1 and τ2) assigned τ1 and τ2 to the intramolecular vibrational relaxation (IVR) (τ1 = ~3 ps) from the initially populated local excited state (FC state) and the S1 → excimer transition (231 ps in n-hexane and 24.3 ps in acetonitrile), respectively. Consequently, our results are more consistent with the scenario that the SF dynamics in Anti-DPyB and Syn-DPyB proceed through an excimer-mediated process rather than a direct SF mechanism caused by strong coupling between the S1 state and free triplet state. This result may indicate that the coupling between the S1 state and free triplet state in CLDs such as Anti-DPyB and Syn-DPyB is weaker than in the molecules that showed such direct SF processes. The Singular values weighted rSVs were globally fitted by exponential functions. The number of exponentials (four exponentials for Anti-DPyB, three exponentials for Syn-DPyB) and constants are shown in Table 2.  Figure S27. Photoinduced reaction schemes for Anti-DPyB containing a direct SF process from the S1 state to the free triplet state. (S0: ground state, FC: Franck-Condon state, S1: singlet excited state, (T1T1): correlated triplet pair, and T1: free triplet state).